Question: Solve for $x$ and $y$ using elimination. ${3x-y = 20}$ ${-5x+y = -36}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-2x = -16$ $\dfrac{-2x}{{-2}} = \dfrac{-16}{{-2}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {3x-y = 20}\thinspace$ to find $y$ ${3}{(8)}{ - y = 20}$ $24-y = 20$ $24{-24} - y = 20{-24}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {-5x+y = -36}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + y = -36}$ ${y = 4}$